The empirical dielectric decay function γ(t)= exp –(t/τ₀)^β may be transformed analytically to give the frequency dependent complex dielectric constant if β is chosen to be 0.50. The resulting dielectric constant and dielectric loss curves are non-symmetrical about the logarithm of the frequency of maximum loss, and are intermediate between the Cole-Cole and Davidson-Cole empirical relations. Using a short extrapolation procedure, good agreement is obtained between the empirical representation and the experimental curves for the α relaxation in polyethyl acrylate. It is suggested that the present representation would have a general application to the α relaxations in other polymers. The Hamon approximation, with a small applied correction, is valid for the present function with β= 0.50 in the range log(ωτ₀) > –0.5, but cannot be used at lower frequencies.

The empirical dielectric decay function ϕ(t)= exp –(t/τ₀)^β, 0< β⩽1 has been transformed analytically and numerically into the frequency dependent complex dielectric permittivity. It is shown that empirical curves give a very satisfactory representation of the dielectric α relaxations observed in polyethyl acrylate, polyvinyl acetate, polyvinyl octanoate, polymethyl acrylate, polypropylene oxide and amorphous polyethylene terephthalate. It is suggested that the present empirical representation is far more satisfactory than existing functions for non-symmetrical loss curves. It is also suggested that the success of the empirical representation may imply that the dipole moment correlation function is a non exponential decay function of time rather than arising from a weighted sum of exponential decay functions. In addition the accuracy of the transformation of transient data into frequency domain data—via the Hamon approximation, is examined for the empirical representation, and it is shown that the transform is accurate for log ωτ₀ > 0, but significant corrections may have to be applied for β >0.5 and log ωτ₀ < 0.